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A151320 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, 1), (1, -1), (1, 0), (1, 1)} 0
1, 3, 13, 58, 270, 1280, 6150, 29805, 145360, 712206, 3501803, 17264747, 85302729, 422197260, 2092558843, 10383452493, 51573082768, 256362474771, 1275210602985, 6346900307554, 31605149836728, 157449319326981, 784667701737738, 3911759095866487, 19506630908252765, 97297440023869383 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

MATHEMATICA

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

CROSSREFS

Sequence in context: A296771 A270786 A151226 * A151227 A151228 A268596

Adjacent sequences:  A151317 A151318 A151319 * A151321 A151322 A151323

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 4 15:43 EDT 2020. Contains 335448 sequences. (Running on oeis4.)